Question

The displacement-time graphs of two particles $A$ and $B$ are straight lines making angles of $30^{\circ }$ and $60^{\circ }$ respectively with the time axis. If the velocity of $A$ is $v_A$ and that of $B$ is $v_B$, the value of $v_A/v_B$ is

• A. $1/2$
• B. $1/\sqrt{3}$
• C. $\sqrt{3}$
• D. $1/3$

Answer 1

Answer: (D)

$v_A=\tan 30^{\circ }$ and $v_B=\tan 60^{\circ }$
$\therefore \frac{v_A}{v_B}=\frac{\tan 30^{\circ }}{\tan 60^{\circ }}=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}$